Question

the perimeter of the rectangle is 34 cm. the perimeter of the triangle is 30 cm. find the value of m. a. 5 cm b. 7 cm c. 6 cm d. 8 cm please select the best answer from the choices provided

Explanation:

Step1: Write rectangle perimeter formula

The perimeter formula for a rectangle is $P = 2(m + n)$. Given $P = 34$, so $2(m + n)=34$, which simplifies to $m + n=17$, thus $n = 17 - m$.

Step2: Write triangle perimeter formula

The perimeter formula for the right - triangle is $P=m + n+(n + 1)$. Given $P = 30$, so $m + n+(n + 1)=30$, which simplifies to $m+2n+1 = 30$ or $m + 2n=29$.

Step3: Substitute $n$ into triangle formula

Substitute $n = 17 - m$ into $m + 2n=29$. We get $m+2(17 - m)=29$.
Expand: $m + 34-2m=29$.
Combine like terms: $-m=29 - 34=-5$.
Multiply both sides by - 1: $m = 5$.

Answer:

A. 5 cm