Find the area $ A $ of a rectangle if side $a = 21$ and diagonal $d = 28$.
Answer
$A = 147 \sqrt{ 7 }$
Explanation
STEP 1: find side $ b $
To find side $ b $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $ a = 21 $ and $ d = 28 $ we have:
$$ 21^2 + b^2 = 28^2 $$ $$ b^2 = 28^2 - 21^2 $$ $$ b^2 = 784 - 441 $$ $$ b^2 = 343 $$ $$ b = \sqrt{ 343 } $$$$ b = 7 \sqrt{ 7 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = a \cdot b $$After substituting $ a = 21 $ and $ b = 7 \sqrt{ 7 } $ we have:
$$ A = 21 \cdot 7 \sqrt{ 7 } $$$$ A = 21 \cdot 7 \sqrt{ 7 } $$$$ A = 147 \sqrt{ 7 } $$This page was created using
Rectangle Calculator