Question

The area of a triangle is the same as area of the square. If the area of a square is 100 cm2 and the corresponding height of a triangle is 5 cm, then the base of the triangle is_____ *​

Answer 1

Answer :

• Base of the triangle is 40 cm.

Given :

• Area of a triangle is the same as area of the square.

• Area of the square = 100 cm²

• Corresponding height of the triangle = 5 cm

To calculate :

• Base of the triangle.

Calculation :

Let the base be "b".

According to the question,

• Area of a triangle is the same as area of the square.

So, linear equation is :

➛ Area of the triangle = Area of the square

Putting the formula of area of both triangle and area of square in LHS and RHS.

➛ $\sf { \dfrac{1}{2} }$ × b cm × h cm = Side × Side

➛ $\sf { \dfrac{1}{2} }$ × b cm × h cm = 100 cm²

[ As area of the square is given 100 cm². ]

➛ $\sf { \dfrac{1}{2} }$ × b cm × 5 cm = 100 cm²

[ As height of the triangle is given 5 cm. ]

Transposing 5 from LHS to RHS

➛ $\sf { \dfrac{1}{2} }$ × b cm = $\sf {\cancel{\dfrac{100 \: {cm}^{2}}{5 \:cm }} }$

➛ $\sf { \dfrac{1}{2} }$ × b cm = 20 cm

Transposing 2 from LHS to RHS.

➛ (1 × b) cm = (20 × 2) cm

➛ b cm = 40 cm

Henceforth, base of the triangle is 40 cm.

Verification :

According to the question,

➛ Area of the triangle = Area of the square

➛ $\sf { \dfrac{1}{2} }$ × b cm × h cm = 100 cm²

➛ $\sf { \dfrac{1}{2} }$ × 40 cm × 5 cm = 100 cm²

➛ 1 × 20 cm × 5 cm = 100 cm²

➛ 100 cm² = 100 cm²

LHS = RHS,

Hence, verified!

Answer 2

Refer the attached image for the answer

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