Question

Find the area and the perimeter of the rectangle, whose length is $15$ cm and the length of one diagonal is $17$ cm.

Answer 1

Given

$L=15$ (Length = L;B = Breadth;H = diagonal)

$H=17$ cm

$L^2+B^2=H^2$

$\Rightarrow (15{)}^2+B^2=(17{)}^2$

$\Rightarrow 225+B^2=289$

$\Rightarrow B^2=289-225$

$\Rightarrow B^2=64$

$\Rightarrow B=\sqrt{64}$

$\Rightarrow B=8cm.$

Breadth $=8cm.$

Area of rectangle =$L\times B=15\times 8=120m^2.$

Perimeter of rectangle $=2(L+B)$

$=2(15+8)$

$=2\left(23\right)$

$=46cm.$