Chapter 11.1, Problem 15CE

(a)

To determine

To Find: The area of each rectangle.

Answer to Problem 15CE

  $25c{m}^2,16c{m}^2,24c{m}^2$

Explanation of Solution

Given: Draw three non-congruent triangles each with perimeter $20cm$ .

Since the triangles are non-congruent, their dimensions are different.

But the perimeter must be $20cm$

So

  $\begin{array}{l}P=2(l+b)\\ 20=2(l+b)\\ l+b=10cm\end{array}$

i.e.

We must take the values of length and width in such a way that their sum is $10cm$

Thus

  $\begin{array}{l}(i)l=5cm,b=5cm\\ (ii)l=8cm,b=2cm\\ (iii)l=6cm,b=4cm\end{array}$

Area of rectangles

  $\begin{array}{l}(i)l=5cm,b=5cm\\ A=lb\\ A=(5)(5)\\ A=25c{m}^2\\ (ii)l=8cm,b=2cm\\ A=lb\\ A=(8)(2)\\ A=16c{m}^2\\ (iii)l=6cm,b=4cm\\ A=lb\\ A=(6)(4)\\ A=24c{m}^2\end{array}$

  

Hence, Area of triangles are $25c{m}^2,16c{m}^2,24c{m}^2$

(b)

To determine

To Find: Which one has the greatest area?

Answer to Problem 15CE

The rectangle having $l=5cm,b=5cm$ has the greatest area.

Explanation of Solution

Given: Three non-congruent triangles each with perimeter $20cm$ .

  $\begin{array}{l}(i)l=5cm,b=5cm\\ A=25c{m}^2\\ (ii)l=8cm,b=2cm\\ A=16c{m}^2\\ (iii)l=6cm,b=4cm\\ A=24c{m}^2\end{array}$

Hence, the rectangle having $l=5cm,b=5cm$ has the greatest area.