Question

The area of rhombus is equal to the area of a triangle whose base and the corresponding altitude are 25m and 16 m respectively. If one of the diagonals of the rhombus is 40 m, find the length of the other diagonal.

Answer 1

Area of triangle = $\frac{1}{2}bh$
Area of rhombus = $\frac{1}{2}d_1d_2$
where d₁ and d₂ are the diagonals of a rhombus.

given that b=25, h=16 and d₁=40

$\frac{1}{2} bh= \frac{1}{2} d_1d_2\\ \\ \Rightarrow 25 \times 16=40 \times d_2\\ \\ \Rightarrow d_2= \frac{25 \times 16}{40}\\ \\ \Rightarrow d_2 =\boxed{40m}$

Length of other diagonal is 40m.

Answer 2

Step-by-step explanation:

$b = 16m \\ h = 25m \\ d {}^{1} = 40m \\ let \: d {}^{2} \: be \: x \\ area \: of \: rhombus = b \times h \\ or \\ area \: of \: rhombus = \frac{1}{2} \times d {}^{1} \times d {}^{2} \\ this \: implies \\ b \times h = \frac{1}{2} \times d^{1} \times x \\ 16 \times 25 = \frac{1}{2} \times 40 \times x \\ \frac{16 \times 25}{40} \times 2 = x \\ 4 \times 5 = x \\ x = 20$