Question

A cafe serves sandwiches in the shape of an isosceles triangle. The ratio of the median of these given sandwiches are 3:2, and the ratio of the bases of these sandwiches is 7:4. What is the ratio of their area?

• A. 21:8
• B. 21:9
• C. 35:16
• D. 25:8

Answer 1

The correct option is A 21:8

For an isosceles triangle, the median is the same as its height.

Ratio of the medians of these triangles = 3:2
Ratio of the base of these triangles = 7:4
Let's take the median of the bigger triangle as 3x, and its base as 7y.

So, the median of the smaller triangle is 2x, and the base of the smaller triangle is 4y.


$\text{Area of a triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$

Let the area of the bigger triangle be A.
Let the area of the smaller triangle be B.

On putting values, we get:
$\text{A}=\frac{1}{2}\times \text{7y}\times \text{3x}$

$\Rightarrow \text{A}=\frac{21xy}{2}$

and,

$\text{B}=\frac{1}{2}\times \text{4y}\times \text{2x}$

$\Rightarrow \text{B}=\frac{8xy}{2}$

So, the ratio of A and B is:

$\frac{\text{A}}{\text{B}}=\frac{\text{21xy}÷\text{2}}{\text{8xy}÷\text{2}}$

$\Rightarrow \frac{\text{A}}{\text{B}}=\frac{\text{21xy}}{\text{8xy}}$

$\Rightarrow \frac{\text{A}}{\text{B}}=\frac{\text{21}}{\text{8}}$

$\Rightarrow \text{A : B}=21:8$