Question

for each shape below, find x.
(a) perimeter = 38cm
(b) perimeter = 30cm
(c) perimeter = 85.5cm
(d) perimeter = 46cm
(e) perimeter = 24cm
(f) perimeter = 162cm

Explanation:

Step1: Recall perimeter formula

The perimeter of a polygon is the sum of the lengths of its sides.

Step2: Solve for (a)

For the isosceles triangle in (a), the perimeter $P=x+(x + 10)+(x + 10)$. Given $P = 38$, we have the equation $x+(x + 10)+(x + 10)=38$. Combine like - terms: $3x+20 = 38$. Subtract 20 from both sides: $3x=38 - 20=18$. Divide both sides by 3: $x = 6$.

Step3: Solve for (b)

For the isosceles triangle in (b), $P=(2x + 1)+(2x + 1)+(10 - x)$. Given $P = 30$, we get $(2x + 1)+(2x + 1)+(10 - x)=30$. Combine like - terms: $3x+12 = 30$. Subtract 12 from both sides: $3x=30 - 12 = 18$. Divide both sides by 3: $x = 6$.

Step4: Solve for (c)

For the isosceles triangle in (c), $P=(2x + 7)+(2x + 7)+(x + 9)$. Given $P = 85.5$, we have $(2x + 7)+(2x + 7)+(x + 9)=85.5$. Combine like - terms: $5x+23 = 85.5$. Subtract 23 from both sides: $5x=85.5 - 23=62.5$. Divide both sides by 5: $x = 12.5$.

Step5: Solve for (d)

For the parallelogram in (d), opposite sides are equal. So $P = 2(x + 9)+2(x - 2)$. Given $P = 46$, we have $2(x + 9)+2(x - 2)=46$. Expand: $2x+18+2x - 4 = 46$. Combine like - terms: $4x + 14 = 46$. Subtract 14 from both sides: $4x=46 - 14 = 32$. Divide both sides by 4: $x = 8$.

Step6: Solve for (e)

For the right - triangle in (e), $P=(x + 5)+(x + 7)+(5x + 5)$. Given $P = 24$, we get $(x + 5)+(x + 7)+(5x + 5)=24$. Combine like - terms: $7x+17 = 24$. Subtract 17 from both sides: $7x=24 - 17 = 7$. Divide both sides by 7: $x = 1$.

Step7: Solve for (f)

For the hexagon in (f), $P=4x+2(2x + 1)$. Given $P = 162$, we have $4x+2(2x + 1)=162$. Expand: $4x+4x+2 = 162$. Combine like - terms: $8x+2 = 162$. Subtract 2 from both sides: $8x=162 - 2 = 160$. Divide both sides by 8: $x = 20$.

Answer:

(a) $x = 6$
(b) $x = 6$
(c) $x = 12.5$
(d) $x = 8$
(e) $x = 1$
(f) $x = 20$