Question

Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.

Answer 1

Given; a rectangle whose length is 150 m and the diagonal is 170 m.

To Find; Perimeter of the rectangle

Solution; Length of rectangle =l

Breath of rectangle = b

Diagonal of rectangle = d

In rectangle length breath and diagonal form a triangle in which we can easily apply Pythagoras theorem

according to Pythagoras theorem

l² + b² = d²

22500+b² = 28900

b²=6400

b=80

Perimeter of rectangle =2(l+b)

=2(80+150)

=460

Hence the perimeter is 460 m

Answer 2

We need to recall the following definitions.

• Pythagoras theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
• Perimeter of rectangle: Sum of all the sides of a rectangle.
• Formula : $Perimeter=2(Length+Width)$

This problem is about the Pythagoras theorem and the perimeter of a rectangle.

Given:

Length of rectangle $=150\space\ m$

Length of diagonal $=170\space\ m$

Apply the Pythagoras theorem in Δ$ABC$ , we get

$AB^{2}+BC^{2}=AC^{2}$

$(150)^2+x^{2}=(170)^2$

$x^{2} =(170)^2-(150)^2$

$x^{2} =28900-22500$

$x^{2} =6400$

$x=80$

Thus, the width of a rectangle is $80\space\ m$.

From the formula of the perimeter of a rectangle, we get

$P=2(150+80)$

$P=2(230)$

$P=460\space\ m$

Hence, the perimeter of a rectangle is $460\space\ m$.