Question

if the side of a square is (1/3)a+(4/5)b , its area would be:
Please tell fast​

Answer 1

Answer -

• The area of the square is (1/9) a + (8/15) ab + (16/25) b².

To find -

• The area of the square.

Step-by-step explanation -

• Here, the side of a square is given to us. We have to find it's area!

We know that -

$\underline{\boxed{\sf Area_{(square)} = (Side)^2}}$

Here,

• Side = (1/3) a + (4/5) b.

Therefore,

$\rm Area_{(square)} = (Side)^2$

$\rm Area_{(square)} = \bigg(\dfrac{1}{3} a + \dfrac{4}{5} b \bigg)^{2}$

$\rm Area_{(square)} = \bigg(\dfrac{1}{3} a + \dfrac{4}{5}b \bigg) \bigg( \dfrac{1}{3}a + \dfrac{4}{5} b \bigg)$

$\rm Area_{(square)} = \bigg(\dfrac{1}{3} a \bigg) \bigg( \dfrac{1}{3} a \bigg) + \bigg(\dfrac{1}{3} a \bigg) \bigg(\dfrac{4}{5} b \bigg) + \bigg(\dfrac{4}{5} b \bigg) \bigg(\dfrac{1}{3} a \bigg)+ \bigg(\dfrac{4}{5} b \bigg) \bigg(\dfrac{4}{5} b \bigg)$

$\rm Area_{(square)} = \dfrac{1}{9} {a}^{2} + \dfrac{4}{15} ab + \dfrac{4}{15} ab + \dfrac{16}{25} {b}^{2}$

$\rm Area_{(square)} = \dfrac{1}{9} {a}^{2} + \dfrac{8}{15} ab + \dfrac{16}{25} {b}^{2}$

Hence -

• The area of the square is (1/9) a² + (8/15) ab + (16/25) b².

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