Question

aisha is decorating a ballroom ceiling with garland. the width of the rectangular ceiling is 42 feet and the diagonal distance from one corner to the opposite corner is 70 feet. how much garland will aisha need for the length of the ceiling?
feet
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Explanation:

Step1: Apply Pythagorean theorem

Let length = $l$, width $w=42$, diagonal $d=70$. The theorem states $l^2 + w^2 = d^2$. Rearrange to solve for $l$:
$l = \sqrt{d^2 - w^2}$

Step2: Substitute given values

Substitute $d=70$ and $w=42$:
$l = \sqrt{70^2 - 42^2}$

Step3: Calculate squares

Compute the squared terms:
$70^2 = 4900$, $42^2 = 1764$

Step4: Subtract and take square root

Find the difference and its square root:
$l = \sqrt{4900 - 1764} = \sqrt{3136} = 56$

Answer:

56 feet