Question

The area of a triangle is equal to that of a square whose
each side measures 35 cm. Find the side of the triangle
whose corresponding altitude is 28 cm.​

Answer 1

Answer:

87.5

Step-by-step explanation:

area of a square = 35*35 = 1225

so triangle area = 1/2*base * altitude

1/2*x*28=1225

14x=1225

x= 1225/14

x=87.5

Answer 2

• GIVEN:-

Area of a triangle is equal to the area of a square.

Side of the square:- 35 cm.

Altitude of triangle = 28 cm.

• To Find:-

Side of the triangle.

• SOLUTION:-

First let's find the area of the square.

$</strong><strong>\</strong><strong>large</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong>area \: of \: square \: = side \: \times \: side</strong><strong>}</strong><strong>}</strong><strong>$

$</strong><strong>\</strong><strong>large</strong><strong>\</strong><strong>Longrightarrow</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong>area = 35 \times 35</strong><strong>}</strong><strong>}</strong><strong>$

$</strong><strong>\</strong><strong>large</strong><strong>\</strong><strong>green</strong><strong>\</strong><strong>therefore</strong><strong>\</strong><strong>boxed</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong>\</strong><strong>green</strong><strong>{</strong><strong>area = 1225 \: {cm}^{2} </strong><strong>}</strong><strong>}</strong><strong>}</strong><strong>$

As it is said that area of square is equal to area of triangle,

$</strong><strong>\</strong><strong>large</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong>area \: of \: triangle \: = \frac{1}{2} \times base \: \times height</strong><strong>}</strong><strong>}</strong><strong>$

According to the condition,

$</strong><strong>\</strong><strong>large</strong><strong>\</strong><strong>Longrightarrow</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong> \frac{1}{2} \times base \: \times \: height \: = 1225</strong><strong>}</strong><strong>}</strong></p><p><strong>$

$</strong><strong>\</strong><strong>large</strong><strong>\Longrightarrow </strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong>\frac{1}{2} \times b \times \: 28 = 1225</strong><strong>}</strong><strong>}</strong><strong>$

$</strong><strong>\</strong><strong>large</strong><strong>\Longrightarrow</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong> 14 \times b = 1225</strong><strong>}</strong><strong>}</strong><strong>$

$</strong><strong>\</strong><strong>large</strong><strong>\Longrightarrow \:</strong><strong>{</strong><strong>\</strong><strong>sf</strong><strong>{</strong><strong> b = \frac{1225}{14}</strong><strong>}</strong><strong>}</strong><strong>$

$\large\blue\therefore\boxed{\sf{\blue{base=87.5\: cm}}}$

• Now let's verify it:-

Putting the value of base = 87.5 cm

$</u></strong><strong><u>\</u></strong><strong><u>large</u></strong><strong><u> </u></strong><strong><u>\Longrightarrow \: </u></strong><strong><u>{</u></strong><strong><u>\</u></strong><strong><u>sf</u></strong><strong><u>{</u></strong><strong><u>\frac{1}{2} \times 87.5 \times 28 = 1225</u></strong><strong><u>}</u></strong><strong><u>}</u></strong><strong><u>$

$</u></strong><strong><u>\</u></strong><strong><u>large</u></strong><strong><u>\Longrightarrow \: </u></strong><strong><u>{</u></strong><strong><u>\</u></strong><strong><u>sf</u></strong><strong><u>{</u></strong><strong><u>87.5 \times 14 = 1225</u></strong><strong><u>}</u></strong><strong><u>}</u></strong><strong><u>$

$</u></strong><strong><u>\</u></strong><strong><u>large</u></strong><strong><u>\Longrightarrow \:</u></strong><strong><u>{</u></strong><strong><u>\</u></strong><strong><u>sf</u></strong><strong><u>{</u></strong><strong><u> 1225 = 1225</u></strong><strong><u>}</u></strong><strong><u>}</u></strong><strong><u>$

As,

$</u></strong><strong><u>\</u></strong><strong><u>large</u></strong><strong><u>{</u></strong><strong><u>\</u></strong><strong><u>sf</u></strong><strong><u>{</u></strong><strong><u>L</u></strong><strong><u>HS</u></strong><strong><u> = </u></strong><strong><u>RHS</u></strong><strong><u>}</u></strong><strong><u>}</u></strong><strong><u>$

We can be sure that the side of the triangle is 87.5 cm.

$\huge\pink\therefore\boxed{\sf{\pink{The\: side\: of\: the\: triangle\: is \:87.5 \:cm}}}$