Find the area $ A $ of a rectangle if side $a = 5$ and diagonal $d = 9$.
Answer
$A = 10 \sqrt{ 14 }$
Explanation
STEP 1: find side $ b $
To find side $ b $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ a = 5 $ and $ d = 9 $ we have:
$$ 5^2 + b^2 = 9^2 $$ $$ b^2 = 9^2 - 5^2 $$ $$ b^2 = 81 - 25 $$ $$ b^2 = 56 $$ $$ b = \sqrt{ 56 } $$$$ b = 2 \sqrt{ 14 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = a \cdot b $$After substituting $ a = 5 $ and $ b = 2 \sqrt{ 14 } $ we have:
$$ A = 5 \cdot 2 \sqrt{ 14 } $$$$ A = 5 \cdot 2 \sqrt{ 14 } $$$$ A = 10 \sqrt{ 14 } $$This page was created using
Rectangle Calculator