One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm² Class 9

One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm² Class 9

Question 1.

One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm², find the length of the shorter diagonal. Class 9

Solution:

Rhombus is divided into four triangles with equal areas

∵ Area of rhombus = 128 cm² ... [Given]

∴ Area of one triangle = $\frac{128}{4}$ = 32 cm²

Let the length of shorter diagonal be x cm.

∴ Length of longer diagonal will be 2x cm.

∵ Diagonals of thrombus bisect each other at right angles.

∵ Each small triangle is right-angled triangle with base $\frac{x}{2}$ cm and height x cm.

∴ Area of triangle = $\frac{1}{2}$ x base x height

∴ 32 = $\frac{1}{2}$ × $\frac{x}{2}$ × x

∴ 32 = $\frac{x^2}{4}$

∴ x² = 128

∴ x = $\sqrt{128}=\sqrt{64 \times 2}=8 \sqrt{2}$

∴ Length of the shorter diagonal = $8 \sqrt{2}$ cm.