[SOLVED] Finding areas

**lucy2284** · February 9th 2009, 08:11 PM

Hi I need some more help with word problems. I don't know if I can get some help because there are drawings that go with it but I'll explain them as best as I can. Or maybe just some ideas on how to plug it into an equation.

1. Length and area. Find the length y in the figure. The area of the shaded region is given. both pictures are completely shaded. There is an attached picture.

**Soroban** · February 9th 2009, 08:45 PM

Hello, Lucy!

Are you sure that you couldn't figure these out yourself?

Find the length $y$ in the figure.

Code:

                  * - - - - - *
                * |           |
              *   |           |
            *     |           | y    Area: 120 in²
          *       |           |
        *         |           |
      * - - - - - * - - - - - *
            y           y

The triangle has area: . $\tfrac{1}{2}y^2$

The square has area: . $y^2$

The total area is 120 in²: . $\tfrac{1}{2}y^2 + y^2 \:=\:120 \quad\Rightarrow\quad\tfrac{3}{2}y^2 \:=\:120 \quad\Rightarrow\quad y^2 \:=\:80$

Therefore: . $y \:=\:\sqrt{80} \:=\:4\sqrt{5}\text{ in.}$

Code:

                  * - - *
                * |     |
              *   |     |
            *     |     | y    Area: 1200 cm²
          *       |     |
        *         |     |
      * - - - - - * - - *
            y        1

The triangle has area: . $\tfrac{1}{2}y^2$

The rectangle has area: . $y\cdot1 \:=\:y$

The total area is 1200 cm²: . $\tfrac{1}{2}y^2 + y \:=\:1200 \quad\Rightarrow\quad y^2 + 2y - 2400 \:=\:0$

. . which factors: . $(y-48)(y+50) \:=\:0$

. . and has the positive root: . $y \:=\:48$

**lucy2284** · February 10th 2009, 02:47 AM

Thank you so much for your help. I am extremely bad at word problems I have been working on these for the past three days and nothing came to me. I am also a little confused as to where the 2y and 2400 came from in B. Thank you again.

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