Geometry Word Problems
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Question 1 of 2
1. Question
The perimeter of the plot of land below is `98`m
`(i)` What is the length and width of the land?`(ii)` What is the area of the land?-
`(i)` length: (28)`\text(m)`, width: (21)`\text(m)``(ii)` Area: (588)`\text(m)^2`
Hint
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A word problem can be translated into an equation for easier solving.Perimeter of a Rectangle
`P=2l+2w`Area of a Rectangle
`A=lw``(i)` Find the length and width of the land.Slot in the given values into the Perimeter Formula to form an equation`P=98``l=x+7``w=x``P` `=` `2l+2w` Perimeter Formula `98` `=` `2(x+7)+2(x)` Solve for `x``98` `=` `2(x+7)+2(x)` `98` `=` `2x+14+2x` `98` `=` `4x+14` `4x+14` `=` `98` `4x+14` `-14` `=` `98` `-14` Subtract `14` from both sides `4x` `=` `84` `4x``-:4` `=` `84``-:4` Divide both sides by `4` `x` `=` `21`m width of the land Solve for `x+7``x+7` `=` `21+7` Substitute `x` `=` `28`m length of the land `(ii)` Find the area of the land.Slot in the values from part `(i)` into the Area Formula`l=28`m`w=21`m`A` `=` `lw` Area Formula `=` `(28)(21)` `=` `588\text(m)^2` `(i)` length: `28`m, width: `21`m`(ii)` Area: `588\text(m)^2` -
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Question 2 of 2
2. Question
Find the size of each angle in this triangle:
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`3x=` (51)`°``3x+12=` (63)`°``4x-2=` (66)`°`
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A word problem can be translated into an equation for easier solving.Form an equation using the values givenRemember that the sum of all interior angles in a triangle is `180°`Angle `1`: `3x`Angle `2`: `3x+12`Angle `3`: `4x-2`Angle `1+` Angle `2+` Angle `3` `=` `180°` `3x+(3x+12)+(4x-2)` `=` `180°` Solve for `x``3x+(3x+12)+(4x-2)` `=` `180°` `10x+10` `=` `180` `10x+10` `-10` `=` `180` `-10` Subtract `10` from both sides `10x` `=` `170` `10x``-:10` `=` `170``-:10` Divide both sides by `10` `x` `=` `17` Solve for the size of each angleAngle `1`:`3x` `=` `3(17)` `=` `51°` Angle `2`:`3x+12` `=` `3(17)+12` `=` `51+12` `=` `63°` Angle `3`:`4x-2` `=` `4(17)-2` `=` `68-2` `=` `66°` Angle `1`: `51°`Angle `2`: `63°`Angle `3`: `66°` -