Find the area of the figure.
-A rectangle with a perimeter of 70 m and a diagonal length of 25 m
A) $7500 \mathrm {~m} ^ { 2 }$
B) $300 \mathrm {~m} ^ { 2 }$
C) $275 \mathrm {~m} ^ { 2 }$
D) $280 \mathrm {~m} ^ { 2 }$

Question

Find the area of the figure.
-A rectangle with a perimeter of 70 m and a diagonal length of 25 m 
A) $7500 \mathrm {~m} ^ { 2 }$
B) $300 \mathrm {~m} ^ { 2 }$
C) $275 \mathrm {~m} ^ { 2 }$
D) $280 \mathrm {~m} ^ { 2 }$

Quizplus · Accepted Answer

The perimeter of a rectangle is given by $2l + 2w = 70$, where $l$ is the length and $w$ is the width. The area of a rectangle is $A = lw$. To find $l$ and $w$, we can use the Pythagorean theorem since the diagonal splits the rectangle into two right-angled triangles. Thus, $l^2 + w^2 = 25^2$. We don't have direct values for $l$ and $w$, but we can express one in terms of the other using the perimeter equation: $l = 35 - w$. Substituting this into the Pythagorean equation gives us two equations with two variables, which can be solved to find the dimensions of the rectangle. After finding $l$ and $w$, we calculate the area as $A = lw$, which results in $300 \mathrm{m}^2$.

Find the Area of the Figure 7500 m27500 \mathrm {~m} ^ { 2 }7500 m2

Find the Area of the Figure $7500 \mathrm {~m} ^ { 2 }$