Question

Find x,y in the given figures of the dimensions are given in cm: ​

Answer 1

★GIVEN★

• Diagonal = (x + 2) cm.
• Length = x cm.
• Breadth = 12 cm.

★To Find★

The value of x.

★SOLUTION★

We know that diagonal of a rectangle,

$\large{\green{\underline{\boxed{\bf{Diagonal=\sqrt{{(Length)}^{2}+{(breadth)}^{2}}}}}}}$

According to the question,

$\large\implies{\sf{Diagonal=\sqrt{{(Length)}^{2}+{(breadth)}^{2}}}}$

$\large\implies{\sf{x+2=\sqrt{{(x)}^{2}+{(12)}^{2}}}}$

Squaring both the sides,

$\large\implies{\sf{{(x+2)}^{2}={(x)}^{2}+{(12)}^{2}}}$

$\large\implies{\sf{{x}^{2}+4x+4={x}^{2}+144}}$

$\large\implies{\sf{\cancel{{x}^{2}}\:+4x+4=\:\cancel{{x}^{2}}+144}}$

$\large\implies{\sf{4x+4=144}}$

$\large\implies{\sf{4x=144-4}}$

$\large\implies{\sf{4x=140}}$

$\large\implies{\sf{x=\dfrac{140}{4}}}$

$\large\implies{\sf{x=\dfrac{\cancel{140}}{\cancel{4}}}}$

$\large\therefore\boxed{\bf{x=35\:cm.}}$

So,

• Breadth = 12 cm.
• Length = x = 35 cm.
• Diagonal = x + 2 = 35 + 2 = 37 cm.

The value of x is 35 cm.