Question

a rectangular field has diagonal of length 17m and perimeter 48

Answer 1

$\huge\underline\mathfrak{Question:}$

Length of a rectangular field is 15m and diagonal is of length 17m. Find its area and perimeter.

$\huge\underline\mathfrak{Explanation:}$

Let ABCD be a rectangle such that

Length of a rectangle (AB) = 15m.

Breadth of a rectangle (BC) = x m.

Join the diagonal AC of a rectangle = 17m (given)

Now,

$\sf{AB^2+BC^2=AC^2}$

$\implies$$\sf{(15)^2+x^2=(17)^2}$

$\implies$$\sf{x^2=(17)^2-(15)^2}$

$\implies$$\sf{x^2=(289-225)m^2}$

$\implies$$\bold{\boxed{\sf{\green{x^2=64\:m^2}}}}$

$\implies$$\sf{x=8m}$

•°• Breadth of a rectangle (BC) = 8m

Area of a rectangle ABCD = length $\times$ breadth

= 15m $\times$ 8m = 120 m².

Perimeter of a rectangle ABCD = $\sf{2(Length+Breadth)}$

=$\sf{2(15m+8m)}$

=$\sf{2(23)}$

$\bold{\large{\boxed{\sf{\red{46m}}}}}$