As one angle is 90°so we are using the Pythagoras theorem in this question. For example, the diagonal of a rectangle of length 6m and width 2m is given by d (6² 2²). Note: In such questions, you may get confused while calculating the breadth of the rectangle with length and the diagonal given. The formula to find the diagonal of a rectangle is d (l² w²), where l is the length and w is the width of the rectangle. $ \Rightarrow $Area of the rectangle = 20$ \times $15 = 300 $cm^2$. Now, we know that the formula of the area of the rectangle is given by:Īrea of the rectangle = length of the rectangle $ \times $ breadth of the rectangle. Therefore, the breadth of the rectangle is 15 cm. On putting the values of the diagonal and length of the rectangle, we get It joins two opposite corners of a square, rectangle, cube, cuboid, or polygon. Using the Pythagoras theorem in the $\vartriangle ABC$ to calculate the value of the breadth of the rectangle, we get Diagonal is a slanting line intersecting the opposite angles of any figure. As we know that $\angle $ABC is 90°, therefore $\vartriangle ABC$ is a right – angled triangle. Then find the size of the television whose dimensions are 16 inches and 40 inches. Example 2: The size of the screen of a television is the length of its diagonal. Answer: The length of each diagonal 10 units. So they are uniquely determined by the given area and given length of the diagonal from which the figure was constructed.Īlternatively, you can choose one of the intersections that is not used in the figure above, but that just gives you a congruent rectangle in a different orientation.Let ABCD be a rectangle and AC be one of the diagonals of the rectangle. Using the diagonal of a rectangle formula, d ( l 2 w 2) d ( 8 2 6 2) 100. The lengths of the sides of this rectangle are uniquely determined by the distance from the intersection point to the two ends of the diameter. How do I calculate the diagonal of a rectangular prism How to calculate volumes of the other solids Thanks to our rectangular prism calculator, you can easily find the cuboid volume, surface area, and rectangular prism diagonal. A right triangle with the given hypotenuse and height $h$ from that hypotenuse must have its right-angle vertex at one of the intersections of one of those lines with the circle.Ĭhoose one such intersection and the rectangle is determined as shown in the figure below. To find the other two vertices, we construct two lines parallel to the diameter at a distance $h$ from the diameter. So for a given diagonal of length $d,$ a rectangle with that diagonal must have two vertices at the ends of the diagonal and the other two lying on the circle with that diameter as shown in the figure below. If the heights are greater than $h$ the area will be too large and if they are less than $h$ the area will be too small.Ī fact about right triangles is that for a given hypotenuse $AB$, the right-angled vertex of the triangle always lies on the circle that has the segment $AB$ as its diameter. That is, diagonal $d$ and area $hd,$ must also be cut into two right triangles by its diagonal, each right triangle having hypotenuse $d$ and height $h$. The area of each triangle is $\frac12 hd,$ and the area of the entire rectangle is $hd.$ Any other rectangle with the same length diagonal and the same area, Since the two triangles are congruent, they have the same altitude, which is labeled $h$ in the figure. The diagonal of length $d$ cuts the rectangle into two right triangles.Įach right triangle has some altitude measured from its right angle to the hypotenuse. Solve Applications Using Properties of Triangles In this section we will use some common geometry formulas. If you missed this problem, review Exercise 1.9.10. Take a given rectangle as shown in the figure below. If you missed this problem, review Exercise 2.6.10. In addition to the algebraic proofs, you can also demonstrate this with a geometric construction.
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