Strawberries and peas
Weekly Problem 17 - 2017
Yasmin lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by $15m^2$. What was the original area of her pea bed?
Yasmin lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by $15m^2$. What was the original area of her pea bed?
Age
11 to 14
Challenge level
Problem
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Yasmin has beds for peas and strawberries in her garden,
as shown in the diagram on the right.
This year, Yasmin moved the boundary:
She decided to change the rectangular pea bed into a square, by lengthening one of its sides by $3\text{m}$.
As a result of this, the area of the strawberry patch was reduced by $15\text{m}^2$.
What was the original area of the pea bed, before the change in the boundary?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 10 m $^2$
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Image
Image
New pea patch is square
Original side length: 5 $-$ 3 = 2 m
Original area: 2 m$\times$5 m = 10 m$^2$