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I am struggling to get some traction on this and need someone to show me how to calculate this. I have a GCSE question that asks:

enter image description here

In the attached image I'm being asked the following:

The arrowhead has an area of $3.6cm^2$. Find the length $x$.

Dan
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  • It looks like if you add the red line to the arrow, you get an equilateral triangle, and the central points is at distance $x$ from each vertex. Without some such assumption, I don't see how to solve the problem. – saulspatz Nov 03 '18 at 18:24

2 Answers2

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The area $3.6cm^2$ is the area of the larger triangle minus the area of the smaller triangle.

$1.5\cdot h - 1.5\cdot (h - x) = 3.6$

$1.5h - 1.5h + 1.5x = 3.6$

$1.5x = 3.6$

$x = 2.4$cm

Phil H
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  • Thanks for that. It’s the only way I could work that out and it is the right answer. I refused to accept it as I couldn’t see how 1.5 could be the base of the triangle since it was angled. But your statement that 3.6cm^2 is the larger triangle proved profound as from the question there was no way I could see that could be derived unless I just took that assumption. – Dan Nov 03 '18 at 18:56
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Hint

You can divide the area in two triangles. You can consider $x$ as the basis and thus the height is $1.5$ cm.

mfl
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